The Weierstrass Function is a famous example of a continuous function that is nowhere differentiable. This means that, while the function does not have any breaks or jumps, it is so "wiggly" that you cannot find a tangent line at any point. It was introduced by the mathematician Karl Weierstrass in the 19th century to illustrate the concept of continuity without differentiability. The function is constructed using an infinite series of sine functions, which oscillate increasingly as they are added together. This unique property challenges the traditional understanding of functions in calculus, showing that continuity and differentiability are not always linked.